Effective non-vanishing of global sections of multiple adjoint bundles for quasi-polarized n-folds, II

Abstract

Let m NEF (n) be the smallest positive integer p such that the dimensions of global sections of multiple adjoint bundles h0(m(KX + L)) are strictly greater than zero for any integer m with m ≥ p and any quasi-polarized n-folds (X, L) for which X is a complex normal Gorenstein projective variety with only rational singularities and KX + L is nef. In this paper, we prove that m NEF (n) ≤ 2n - 4 holds for n ≥ 4.